@Andrew: Here's a hint. Conjugation in $GL(n)$ means change-of-basis ... i.e., the conjugacy class is all different matrix representations of a given linear transformation.
@TedShifrin Not a sure thing; depends on the school. My observations suggest foreign language exams being steadily dropped from PhD requirements in math departments around the U.S.
(Observations being visits to grad program pages of math departments.)
Subdivide each simplex in the boundary . Then the subdivision of the simplex is [v_0, ..., v_n, C], where the first are the vertices of one of te subdivided simplices, and C is the centroid
There's a description of this process somewhere in the beginning of chapter 2 of Hatcher's book. It has pictures.
@blue for your favorite positive $\varepsilon$ there's an $f \in O(x^{4+\varepsilon})$ such that for any abelian group $G$, $|\text{Aut}(G \times G)| \leq f(|\text{Aut}(G)|)$.
the argument does not extend to even a little bit more generality
Trivia time: August 27, 2014 was the day with the second-largest number of unique visitors to Math.SE: 136723. The largest number ever: 158465 uniques on April 7, 2014. Interestingly enough, both spikes are due to the same question. (cc: @rschwieb)